Problem: Simplify the following expression: $k = \dfrac{4r^2 + 40r + 36}{r + 1} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ k =\dfrac{4(r^2 + 10r + 9)}{r + 1} $ Then we factor the remaining polynomial: $r^2 + {10}r + {9} $ ${1} + {9} = {10}$ ${1} \times {9} = {9}$ $ (r + {1}) (r + {9}) $ This gives us a factored expression: $\dfrac{4(r + {1}) (r + {9})}{r + 1}$ We can divide the numerator and denominator by $(r - 1)$ on condition that $r \neq -1$ Therefore $k = 4(r + 9); r \neq -1$